On infinite area for complex exponential function

This paper shows via a reduced family of examples, the relaxed Newton's method is applied to complex exponential function F(z)=ze^z and F(z)=ze^z2, the basin of roots has infinite area. In addition, we examined their computer pictures which are fractals for the relaxed Newton's basin. In fact, computer experiments F(z)=P(z)e^z and F(z)=P(z)e^z2, indicate this to hold for arbitrary non-constant polynomial P(z).